Constitutive Law(6 equations, O unknowns) C Bound dary conditions of two types Traction or natural boundary conditions: For tractions t imposed on the portion of the surface of the body aBt Displacement or essential boundary conditions: For displacement

Which of the following expressions most ac curately and simply represents the comple mentary strain energy density Uc of a linear elastic material?

Extend definition to material bodies: total work is the addition of the work done on all particles by forces distributed over the volume W by forces distributed over the surface t·udS

How can the paradox with the spring be plained? In other words, which of the following statements is true 1. Equilibrium can be derived from the equiv alence of the external and the internal work 2. Equilibrium is an artifact of our imagina- tion

Strain energy and potential energy of a beam brec sedans hoMe the neutra xxis remain So Figure 1: Kinematic assumptions for a beam Kinematic assumptions for a beam: From the figure: AA'=u3(a1) Assume small deflections: B B\,BB\=3+ duy

which generalizes to the statement. This reduces the number of material constants from 81 to 54. In a similar fashion we can make use of the symmetry of the strain tensor This further reduces the number of material constants to 36. To further reduce the number of material constants consider the conclusion from the first law for elastic materials, equation

Which of the following expressions represents the rate of work done by the stresses during the deformation of a body of an arbitrary material?

The following stress-strain curves were obtained for dif- ferent materials subjecting the specimen to the loading path(a, b, c, d ). Which one(s) of them correspond to elas- tic material(s)

16.21 Techniques of Structural Analysis and sig Spring 2003 Unit #4- Thermodynamics Principles First Law of Thermodynamics

For the uniform state of plane strain shown in the fig ure,which one(s) of the following statement(s) is(are valid?(Assume Poisson's ratio v+0)